Synchronization in 3D data hiding is one of the main problems. We need to know where we can embed informa- tion, and be able to find this space in order to extract the message. Various algorithms propose synchronization techniques by triangle or vertex path in a 3D mesh. In this paper, we proposed a new synchronization technique based on Euclidean minimum spanning tree computing (EMST) and the analysis of the displacement of the vertices without moving the connections in the tree. Based on the analysis of the vertices, we select the most robust vertices and synchronize these areas by computing a new EMST called "robust EMST". Then, we analyze the robustness of the technique, i.e. the stability of the most robust vertices selection; and demonstrate the consistence of the criterion selection with the vertex displacement.